Higher moments modeling and forecasting

Abstract

This thesis extends the literature on portfolio selection with higher moments by investigating how non-normality of returns and higher moments may affect hedging strategies. In order to account for time varying skewness and kurtosis in optimal hedge ratio estimation, the ARCD model proposed by Hansen (1994) is employed, in which full conditional density is modelled allowing for conditional shape parameters. In a horserace of models, the dynamic hedging effectiveness of the ARCD is compared to that obtained by OLS, error-correction, exponential moving averages, and, univariate and multivariate GARCH. Effectiveness is measured in-sample and out-of-sample using the minimum variance method. Spot and futures daily closing prices are used for stock indices from the US, UK and Germany for the period January 1999 to September 2004. The results suggest that the hedging performance using the ARCD outperforms that obtained by the competing approaches. Also, in this thesis an alternative, simplified multivariate model is proposed, the simplified Multivariate Autoregressive Conditional Density Model (S-ARCD) which is compatible with the skewness and kurtosis of the financial returns and is easy to be implemented increasing the computational efficiency. It is based also, on the Autoregressive Conditional Density Model (ARCD) proposed by Hansen (1994) and involves the estimation only of the univariate specification of the above model. The conditional variances are calculated by the simple univariate models, and the conditional covariance is then imputed from these variance estimates. The S-ARCD is illustrated to forecast the VaR of aggregate equity portfolios for the US and UK and foreign exchange portfolio for EUR and GBP against USD and is compared to the ad hoc multivariate version of GARCH (Wang, Yao, 2005) and BEKK models. The results, using both statistical and economic criteria, suggest that the simplified multivariate version of ARCD performs at least well as the other two models indicating the higher moments’ importance in volatility forecasting and VaR calculation. Finally, the thesis examines the Autoregressive Conditional Density (ARCD) application in combination with the framework of Hasbrouck (1995) in order to investigate empirically the predictive ability of error-correction models based on the cointegration relationship between option and spot prices. Although the cointegration relationship between spot and option prices has been studied in the literature, the implications in terms of error-correction modelling have not yet been empirically examined. Using daily index and option closing prices from the US, France and Germany we identify significant cointegration relationships in each market and estimate nonlinear error-correction models. Also, the role of higher moments in the cointegration relationship is not important. The error-correction model results suggest that both option and spot prices contain information about option price returns.%%%%H διατριβή μeλeτά τις στατιστικές ιδιότητeς και τη μέτρηση κινδύνων…